Finite Group Databasebeta

← Group #13137401

Character table — Group #13137401

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222222222222222226666666612121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order12223444444666121212121212121212121212336666663666121212121212121212121212121212121212121212121212888888882424242424242424242424242424242444441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ611111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ711111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ811111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222-122-1-12-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000220000-1-1-1-1
χ10222222222222222222222222222-122-1-12-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000-2-200001111
χ1122222222222222222222222222-12-1-122-12-1-1-1-1-1-1-1-12222-1-122-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002200-1-1-1-10000
χ1222222222222222222222222222-12-1-122-12-1-1-1-1-1-1-1-12222-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-20011110000
χ132222222-2-2-2-22222222-2-2-2-2-2-2-2-222222222222222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ142222222-2-2-2-22222222-2-2-2-2-2-2-2-22-122-1-12-1-1-1-1-122-2-2-1-111-2-2111111-1-1-1-1111100000000000000000000000000000000−i3i3−i3i3
χ152222222-2-2-2-22222222-2-2-2-2-2-2-2-22-122-1-12-1-1-1-1-122-2-2-1-111-2-2111111-1-1-1-1111100000000000000000000000000000000i3−i3i3−i3
χ162222222-2-2-2-22222222-2-2-2-2-2-2-2-2-12-1-122-12-1-1-1-1-1-11122-2-211-2-21111-1-1-1-111110000000000000000000000000000−i3i3−i3i30000
χ172222222-2-2-2-22222222-2-2-2-2-2-2-2-2-12-1-122-12-1-1-1-1-1-11122-2-211-2-21111-1-1-1-111110000000000000000000000000000i3−i3i3−i30000
χ1822222-2-222-2-2222-2-2-2-22222-2-2-2-2222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ1922222-2-222-2-2222-2-2-2-22222-2-2-2-22-122-1-12-1-1-1-1-1-2-22211-1-1-2-21111111111-1-1-1-100000000000000000000000000000000−i3i3i3−i3
χ2022222-2-222-2-2222-2-2-2-22222-2-2-2-22-122-1-12-1-1-1-1-1-2-22211-1-1-2-21111111111-1-1-1-100000000000000000000000000000000i3−i3−i3i3
χ2122222-2-222-2-2222-2-2-2-22222-2-2-2-2-12-1-122-12-1-1-1-111-1-1-2-22211-2-211111111-1-1-1-10000000000000000000000000000−i3i3i3−i30000
χ2222222-2-222-2-2222-2-2-2-22222-2-2-2-2-12-1-122-12-1-1-1-111-1-1-2-22211-2-211111111-1-1-1-10000000000000000000000000000i3−i3−i3i30000
χ2322222-2-2-2-222222-2-2-2-2-2-2-2-222222-122-1-12-1-1-1-1-1-2-2-2-2111122-1-1-1-1-1-111111111000000000000000000000000002-20000-1-111
χ2422222-2-2-2-222222-2-2-2-2-2-2-2-222222-122-1-12-1-1-1-1-1-2-2-2-2111122-1-1-1-1-1-11111111100000000000000000000000000-22000011-1-1
χ2522222-2-2-2-222222-2-2-2-2-2-2-2-22222-12-1-122-12-1-1-1-11111-2-2-2-2-1-122-1-1-1-1111111110000000000000000000000002-200-1-1110000
χ2622222-2-2-2-222222-2-2-2-2-2-2-2-22222-12-1-122-12-1-1-1-11111-2-2-2-2-1-122-1-1-1-111111111000000000000000000000000-220011-1-10000
χ2722-2-22002-2002-2-2000022-2-20000222-22-2-2-222-2-2002-2002-200000000000022-2-222−2−222−2−22222−2−2−2−22222−2−2−2−2000000000000
χ2822-2-22002-2002-2-2000022-2-20000222-22-2-2-222-2-2002-2002-200000000000022-2-2−2−222−2−222−2−2−2−22222−2−2−2−22222000000000000
χ2922-2-2200-22002-2-20000-2-2220000222-22-2-2-222-2-200-2200-22000000000000-2-22222−2−2−2−2222222−2−2−2−2−2−2−2−22222000000000000
χ3022-2-2200-22002-2-20000-2-2220000222-22-2-2-222-2-200-2200-22000000000000-2-222−2−22222−2−2−2−2−2−222222222−2−2−2−2000000000000
χ312-22-222-20000-22-222-2-20000000022-22-22-2-22-22-22-2002-2000000000022-2-200002−22−22−22−222−2−222−2−222−2−222−2−2000000000000
χ322-22-222-20000-22-222-2-20000000022-22-22-2-22-22-22-2002-2000000000022-2-20000−22−22−22−22−2−222−2−222−2−222−2−222000000000000
χ332-22-22-220000-22-2-2-2220000000022-22-22-2-22-22-2-2200-220000000000-2-22200002−22−2−22−2222−2−222−2−2−2−222−2−222000000000000
χ342-22-22-220000-22-2-2-2220000000022-22-22-2-22-22-2-2200-220000000000-2-2220000−22−222−22−2−2−222−2−22222−2−222−2−2000000000000
χ352-2-22200002-2-2-220000000022-2-222-2-2-2-2222-2-22000000002-22-222-2-20000000000002-2-220000000022-2-2-2-222000000000000
χ362-2-22200002-2-2-220000000022-2-222-2-2-2-2222-2-22000000002-22-222-2-2000000000000-222-200000000-2-22222-2-2000000000000
χ372-2-2220000-22-2-2200000000-2-22222-2-2-2-2222-2-2200000000-22-22-2-222000000002-2-22000022-2-2-2-22200000000000000000000
χ382-2-2220000-22-2-2200000000-2-22222-2-2-2-2222-2-2200000000-22-22-2-22200000000-222-20000-2-22222-2-200000000000000000000
χ3944444444444444444444444444-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000
χ404444444-4-4-4-44444444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-21111-2-222-2-2222222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000
χ4144444-4-444-4-4444-4-4-4-44444-4-4-4-4-2-2-2-2-2-2-2-2111122-2-222-2-22222-1-1-1-1-1-1-1-11111000000000000000000000000000000000000
χ4244444-4-4-4-444444-4-4-4-4-4-4-4-44444-2-2-2-2-2-2-2-2111122222222-2-2-2-21111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ4344-4-44004-4004-4-4000044-4-400004-24-4-22-42-2-222004-400-22000000000000-2-222000000000000000000000000000000000000
χ4444-4-44004-4004-4-4000044-4-40000-24-224-42-4-2-22200-22004-4000000000000-2-222000000000000000000000000000000000000
χ4544-4-44004-4004-4-4000044-4-40000-2-2-22-222211-1-100-2200-2200003i−3i3i−3i3i−3i3i−3i11-1-1000000000000000000000000000000000000
χ4644-4-44004-4004-4-4000044-4-40000-2-2-22-222211-1-100-2200-220000−3i3i−3i3i−3i3i−3i3i11-1-1000000000000000000000000000000000000
χ4744-4-4400-44004-4-40000-4-44400004-24-4-22-42-2-22200-44002-200000000000022-2-2000000000000000000000000000000000000
χ4844-4-4400-44004-4-40000-4-4440000-24-224-42-4-2-222002-200-4400000000000022-2-2000000000000000000000000000000000000
χ4944-4-4400-44004-4-40000-4-4440000-2-2-22-222211-1-1002-2002-200003i−3i3i−3i−3i3i−3i3i-1-111000000000000000000000000000000000000
χ5044-4-4400-44004-4-40000-4-4440000-2-2-22-222211-1-1002-2002-20000−3i3i−3i3i3i−3i3i−3i-1-111000000000000000000000000000000000000
χ514-44-444-40000-44-444-4-4000000004-2-442-2-42-22-224-400-220000000000-2-2220000000000000000000000000000000000000000
χ524-44-444-40000-44-444-4-400000000-242-2-442-4-22-22-22004-40000000000-2-2220000000000000000000000000000000000000000
χ534-44-444-40000-44-444-4-400000000-2-22-22-2221-11-1-2200-220000003i−3i−3i3i11-1-13i−3i3i−3i000000000000000000000000000000000000
χ544-44-444-40000-44-444-4-400000000-2-22-22-2221-11-1-2200-22000000−3i3i3i−3i11-1-1−3i3i−3i3i000000000000000000000000000000000000
χ554-44-44-440000-44-4-4-444000000004-2-442-2-42-22-22-44002-2000000000022-2-20000000000000000000000000000000000000000
χ564-44-44-440000-44-4-4-44400000000-242-2-442-4-22-222-200-44000000000022-2-20000000000000000000000000000000000000000
χ574-44-44-440000-44-4-4-44400000000-2-22-22-2221-11-12-2002-20000003i−3i−3i3i-1-111−3i3i−3i3i000000000000000000000000000000000000
χ584-44-44-440000-44-4-4-44400000000-2-22-22-2221-11-12-2002-2000000−3i3i3i−3i-1-1113i−3i3i−3i000000000000000000000000000000000000
χ594-4-44400004-4-4-440000000044-4-44-2-4-4224-2-222-2000000004-4-22-2-22200000000000000000000000000000000000000000000
χ604-4-44400004-4-4-440000000044-4-4-2422-4-4-24-222-200000000-224-4-2-22200000000000000000000000000000000000000000000
χ614-4-44400004-4-4-440000000044-4-4-2-22222-2-21-1-1100000000-22-2211-1-13i−3i−3i3i−3i3i3i−3i000000000000000000000000000000000000
χ624-4-44400004-4-4-440000000044-4-4-2-22222-2-21-1-1100000000-22-2211-1-1−3i3i3i−3i3i−3i−3i3i000000000000000000000000000000000000
χ634-4-4440000-44-4-4400000000-4-4444-2-4-4224-2-222-200000000-442-222-2-200000000000000000000000000000000000000000000
χ644-4-4440000-44-4-4400000000-4-444-2422-4-4-24-222-2000000002-2-4422-2-200000000000000000000000000000000000000000000
χ654-4-4440000-44-4-4400000000-4-444-2-22222-2-21-1-11000000002-22-2-1-1113i−3i−3i3i3i−3i−3i3i000000000000000000000000000000000000
χ664-4-4440000-44-4-4400000000-4-444-2-22222-2-21-1-11000000002-22-2-1-111−3i3i3i−3i−3i3i3i−3i000000000000000000000000000000000000
χ676666-3666666-3-3-3-3-3-3-3-3-3-3-3-3-3-3-300000000000000000000000000000000000022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ686666-3666666-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3000000000000000000000000000000000000-2-2-2-2-2-2-2-21111111111111111000000000000
χ696666-366-6-6-6-6-3-3-3-3-3-3-333333333000000000000000000000000000000000000000000003−33−33−33−33−33−33−33−3000000000000
χ706666-366-6-6-6-6-3-3-3-3-3-3-33333333300000000000000000000000000000000000000000000−33−33−33−33−33−33−33−33000000000000
χ716666-3-6-666-6-6-3-3-33333-3-3-3-33333000000000000000000000000000000000000000000003−33−33−33−3−33−33−33−33000000000000
χ726666-3-6-666-6-6-3-3-33333-3-3-3-3333300000000000000000000000000000000000000000000−33−33−33−333−33−33−33−3000000000000
χ736666-3-6-6-6-666-3-3-333333333-3-3-3-30000000000000000000000000000000000002222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ746666-3-6-6-6-666-3-3-333333333-3-3-3-3000000000000000000000000000000000000-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ7566-6-6-3006-600-33333−3333−33-3-33333−3333−3300000000000000000000000000000000000022−2−222−2−2ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ7666-6-6-3006-600-33333−3333−33-3-33333−3333−33000000000000000000000000000000000000−2−222−2−222−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7000000000000
χ7766-6-6-3006-600-333−3333−3333-3-333−3333−333300000000000000000000000000000000000022−2−222−2−2ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ7866-6-6-3006-600-333−3333−3333-3-333−3333−3333000000000000000000000000000000000000−2−222−2−222−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23000000000000
χ7966-6-6-300-6600-33333−3333−3333-3-3−3333−333300000000000000000000000000000000000022−2−2−2−222ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23000000000000
χ8066-6-6-300-6600-33333−3333−3333-3-3−3333−3333000000000000000000000000000000000000−2−22222−2−2−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ8166-6-6-300-6600-333−3333−333333-3-333−3333−3300000000000000000000000000000000000022−2−2−2−222ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7000000000000
χ8266-6-6-300-6600-333−3333−333333-3-333−3333−33000000000000000000000000000000000000−2−22222−2−2−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ836-66-6-36-600003-33-3-33333−3333−3333−33−33330000000000000000000000000000000000002−22−22−22−2ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ846-66-6-36-600003-33-3-33333−3333−3333−33−3333000000000000000000000000000000000000−22−22−22−22−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000
χ856-66-6-36-600003-33-3-333−3333−3333−333333−330000000000000000000000000000000000002−22−22−22−2ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ866-66-6-36-600003-33-3-333−3333−3333−333333−33000000000000000000000000000000000000−22−22−22−22−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000
χ876-66-6-3-6600003-3333-3-333−3333−33−333333−330000000000000000000000000000000000002−22−2−22−22ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000
χ886-66-6-3-6600003-3333-3-333−3333−33−333333−33000000000000000000000000000000000000−22−222−22−2−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ896-66-6-3-6600003-3333-3-3−3333−333333−33−33330000000000000000000000000000000000002−22−2−22−22ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000
χ906-66-6-3-6600003-3333-3-3−3333−333333−33−3333000000000000000000000000000000000000−22−222−22−2−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ916-6-66-300006-633-333−33−3333−333333−33-3-33300000000000000000000000000000000000000002-2-223−3−33−333−3-1-11111-1-1000000000000
χ926-6-66-300006-633-333−33−3333−333333−33-3-3330000000000000000000000000000000000000000-222-2−333−33−3−3311-1-1-1-111000000000000
χ936-6-66-300006-633-3−333333−3333−33−3333-3-33300000000000000000000000000000000000000002-2-22−333−33−3−33-1-11111-1-1000000000000
χ946-6-66-300006-633-3−333333−3333−33−3333-3-3330000000000000000000000000000000000000000-222-23−3−33−333−311-1-1-1-111000000000000
χ956-6-66-30000-6633-333−33−333333−33−333333-3-30000000000000000000000000000000000002-2-220000-1-11111-1-1−333−33−3−33000000000000
χ966-6-66-30000-6633-333−33−333333−33−333333-3-3000000000000000000000000000000000000-222-2000011-1-1-1-1113−3−33−333−3000000000000
χ976-6-66-30000-6633-3−333333−33−333333−3333-3-30000000000000000000000000000000000002-2-220000-1-11111-1-13−3−33−333−3000000000000
χ986-6-66-30000-6633-3−333333−33−333333−3333-3-3000000000000000000000000000000000000-222-2000011-1-1-1-111−333−33−3−33000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.